Ocular Biomechanics and Simulation

The technology for the simulation and prediction of corneal biomechanical response is based on the PhD thesis of Dr. Harald P. Studer and on research at the University of Bern, Switzerland. The thesis and the associated research papers consist of a mathematical material model, capable of predicting the biomechanical response of the cornea to physical interference. The material model includes

A) Realistic collagen fiber distribution in full 3D

Collagen Fibre Distribution

The collagen fiber distribution in the eye is inhomogeneous, as it varies between the center of the cornea and the periphery. Furthermore, the anterior section of the cornea has a different fiber structure than the deeper layers on the posterior cornea.

B) Collagen cross-links: The main collagen fibers are connected by so called collagen cross-links, giving shear stiffness to the tissue.

C) Non-linear biomechanics: It is well documented in literature that corneal tissue does not have a constant modulus of elasticity. Its moduli rather depend on the degree of deformation. With other words, the more the cornea is deformed, the stiffer it becomes. 

D) Incompressibility: Thanks to its high water content, corneal tissue is nearly incompressible. 

Simulation of the deepness inhomogeneity of corneal tissue

Over the last couple of years it became more and more evident that the cornea is inhomogenous over its thickness profile. Literature shows that while the posterior part of the stroma shows nicely stacked collagen sheets, distribution of the anterior collagen is much more chaotic. Fibers bifurcate, reconnect, and are interwoven with each other. This rather complex ultrastructure results in a much stiffer anterior, and softer posterior cornea.

Deepness Inhomogenities

Left: Depth dependent collagen fibre order. Right: Corneal stiffness, measured with Brillouin microscopy (Winkler 2011, Scarcelli 2012)

The resulting mechanical stiffnesses inhomogeneity over the thickness profile of the cornea has experimentally been quantified by several authors, and we have worked it into our material definition for corneal tissue.

Simulation of viscoelastic tissue properties

Viscoelastic effects include time dependent features of the tissue, such as a loading- undloading hysteresis, and creep/stress relaxation. The image on the left shows how the stress decreases while the displacement is maintained. 

 

 

 

Applied to the cornea, stress relaxation or creep can be seen, for example, by inflating a cornea model with IOP and waiting for some time. The right side image of the two shows how a relaxed cornea deforms further even after no more pressure is being added.